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Two-Lines: The First Valid Test of U-Shaped Relationships

29 Pages Posted: 22 Aug 2017  

Uri Simonsohn

University of Pennsylvania - The Wharton School

Date Written: May 17, 2017

Abstract

Many psychological theories predict u-shaped relationships: x is good in low quantities, but bad in high quantities, or vice-versa. These predictions are tested primarily via quadratic regressions; here I show such approach is essentially never valid. I introduce a new test: estimating a regression with two separate lines, one for ‘low’ and one for ‘high’ values of x. A u-shape is present if the two slopes have opposite sign and are individually significant. A procedure to set the breakpoint for ‘low’ vs ‘high’ is proposed, the Robin Hood algorithm, and shown to be superior to all alternatives considered, including maximizing fit. The problems with the quadratic and advantages of the two-lines are demonstrated via simulations and examples from published psychological research.

Keywords: regression, interactoin, quadratic, u-shape, specification error

Suggested Citation

Simonsohn, Uri, Two-Lines: The First Valid Test of U-Shaped Relationships (May 17, 2017). Available at SSRN: https://ssrn.com/abstract=3021690

Uri Simonsohn (Contact Author)

University of Pennsylvania - The Wharton School ( email )

3730 Walnut Street
JMHH 500
Philadelphia, PA 19104-6365
United States

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